What defines the term 'half-life' in radioactive decay?

The term 'half-life' in radioactive decay is defined as the time required for half of the radioactive atoms in a sample to decay into a different substance. This concept is fundamental in nuclear physics and helps in understanding how quickly a radioactive isotope will decrease in quantity over time. By knowing the half-life of a substance, one can predict how long it will take for the material to diminish to a specific amount, which is particularly important in fields like radiometric dating and medical applications using radioactive tracers.

The other options do not accurately represent the concept of half-life. The total lifespan of a radioactive element encompasses its entire existence from the moment of its formation to complete decay, which is different from the defined time it takes for half of it to decay. Similarly, the period before radioactive waste is considered safe can vary widely based on the type of radionuclide and is not fixed as half-life. Complete radiation shielding is a matter of safety and protection, which relates to reducing exposure rather than defining the decay rate or time. Thus, the correct answer clearly encapsulates the fundamental definition of half-life in the context of radioactive decay.